Problem: Solve for $x$ and $y$ using elimination. ${2x-5y = -19}$ ${x-2y = -6}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $-2$ ${2x-5y = -19}$ $-2x+4y = 12$ Add the top and bottom equations together. $-y = -7$ $\dfrac{-y}{{-1}} = \dfrac{-7}{{-1}}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {2x-5y = -19}\thinspace$ to find $x$ ${2x - 5}{(7)}{= -19}$ $2x-35 = -19$ $2x-35{+35} = -19{+35}$ $2x = 16$ $\dfrac{2x}{{2}} = \dfrac{16}{{2}}$ ${x = 8}$ You can also plug ${y = 7}$ into $\thinspace {x-2y = -6}\thinspace$ and get the same answer for $x$ : ${x - 2}{(7)}{= -6}$ ${x = 8}$